Open mapping theorem (functional analysis)
Condition for a linear operator to be open / From Wikipedia, the free encyclopedia
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In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem[1] (named after Stefan Banach and Juliusz Schauder), is a fundamental result that states that if a bounded or continuous linear operator between Banach spaces is surjective then it is an open map.